A) Erdos Renyi Graph

B) Complemente

C) Adjacency Matrix

Matrix

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                 
 [1,] . . 1 . . . . 1 1 . . . 1 1 . . . 1 . 1 . . . . . . . . . .
 [2,] . . . . . . . . . . . . 1 . . . . . . . . . . 1 . . 1 . . .
 [3,] 1 . . 1 . 1 . 1 1 . . . 1 1 1 . . . . 1 . . 1 . . . . . . .
 [4,] . . 1 . . . . 1 . . 1 . . . . . . . . . . . . . 1 . 1 . . 1
 [5,] . . . . . . 1 1 . 1 . . . . . . . . 1 . . . 1 . . . . . . 1
 [6,] . . 1 . . . . . . . 1 . . . . . 1 . . . . . . . . . . . . .
 [7,] . . . . 1 . . . . . 1 . . . . . 1 . . . . . 1 . 1 . 1 1 . .
 [8,] 1 . 1 1 1 . . . 1 . . 1 . . . . . . . . . . 1 . 1 . . . . .
 [9,] 1 . 1 . . . . 1 . 1 . . . 1 . . . . . . . . . . 1 . 1 . 1 .
[10,] . . . . 1 . . . 1 . . . 1 1 1 1 . . . 1 . 1 . . . . . 1 . .
[11,] . . . 1 . 1 1 . . . . . 1 . . . 1 . . 1 . . . . 1 1 . . . 1
[12,] . . . . . . . 1 . . . . . . . . . . . 1 1 . . 1 . . . . . .
[13,] 1 1 1 . . . . . . 1 1 . . . . . 1 1 1 1 1 . . . 1 . . . . .
[14,] 1 . 1 . . . . . 1 1 . . . . 1 . . . 1 . . . . . . . 1 1 . .
[15,] . . 1 . . . . . . 1 . . . 1 . . . . . . . 1 1 . . . . . . .
[16,] . . . . . . . . . 1 . . . . . . 1 . . . 1 1 1 . . . 1 . . .
[17,] . . . . . 1 1 . . . 1 . 1 . . 1 . 1 . . . . . . 1 . . 1 . 1
[18,] 1 . . . . . . . . . . . 1 . . . 1 . . . . . . . 1 . . . . .
[19,] . . . . 1 . . . . . . . 1 1 . . . . . . 1 . . . . . . . 1 .
[20,] 1 . 1 . . . . . . 1 1 1 1 . . . . . . . . 1 . 1 . 1 . . . 1
[21,] . . . . . . . . . . . 1 1 . . 1 . . 1 . . . . . . . . . . .
[22,] . . . . . . . . . 1 . . . . 1 1 . . . 1 . . . . . . . . . .
[23,] . . 1 . 1 . 1 1 . . . . . . 1 1 . . . . . . . . . . . . . 1
[24,] . 1 . . . . . . . . . 1 . . . . . . . 1 . . . . 1 . . . . .
[25,] . . . 1 . . 1 1 1 . 1 . 1 . . . 1 1 . . . . . 1 . . . . . .
[26,] . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . . . . 1
[27,] . 1 . 1 . . 1 . 1 . . . . 1 . 1 . . . . . . . . . . . . . .
[28,] . . . . . . 1 . . 1 . . . 1 . . 1 . . . . . . . . . . . . 1
[29,] . . . . . . . . 1 . . . . . . . . . 1 . . . . . . . . . . 1
[30,] . . . 1 1 . . . . . 1 . . . . . 1 . . 1 . . 1 . . 1 . 1 1 .

D) Some powers of the matrix

Matrix^2

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                    
 [1,] 7 1  5 2 1 1 . 2 3 4 2 2  3 2 2 . 2 1 2  2 1 1 2 1 4 1 2 1 1 1
 [2,] 1 3  1 1 . . 1 . 1 1 1 1  . 1 . 1 1 1 1  2 1 . . . 2 . . . . .
 [3,] 5 1 10 1 2 . 1 4 3 5 4 2  2 3 2 1 2 2 2  2 1 2 2 1 4 1 3 1 1 3
 [4,] 2 1  1 6 2 2 3 2 4 . 2 1  3 2 1 1 3 1 .  3 . . 3 1 2 2 . 1 1 1
 [5,] 1 .  2 2 6 . 1 1 2 . 2 1  2 2 2 2 2 . .  2 1 1 3 . 2 1 1 3 2 1
 [6,] 1 .  . 2 . 3 2 1 1 . 1 .  3 1 1 1 1 1 .  2 . . 1 . 2 1 . 1 . 2
 [7,] . 1  1 3 1 2 7 3 2 2 2 .  3 2 1 3 3 2 1  1 . . 1 1 2 1 . 1 . 5
 [8,] 2 .  4 2 1 1 3 8 3 2 2 .  3 3 2 1 1 2 1  3 1 . 2 2 2 . 2 . 1 3
 [9,] 3 1  3 4 2 1 2 3 8 1 1 1  4 4 3 2 1 2 2  3 . 1 2 1 1 . 1 2 . 1
[10,] 4 1  5 . . . 2 2 1 9 2 1  1 3 2 1 3 1 3  2 2 3 3 1 2 1 3 1 1 3
[11,] 2 1  4 2 2 1 2 2 1 2 9 1  3 . . 1 5 3 1  3 1 1 2 2 4 2 2 3 1 4
[12,] 2 1  2 1 1 . . . 1 1 1 4  2 . . 1 . . 1  1 . 1 1 1 2 1 . . . 1
[13,] 3 .  2 3 2 3 3 3 4 1 3 2 11 4 2 3 3 3 1  4 1 2 1 3 3 2 1 2 1 3
[14,] 2 1  3 2 2 1 2 3 4 3 . .  4 8 2 2 1 1 .  3 1 2 2 . 1 . 1 1 2 1
[15,] 2 .  2 1 2 1 1 2 3 2 . .  2 2 5 3 . . 1  3 . 1 1 . . . 1 2 . 1
[16,] . 1  1 1 2 1 3 1 2 1 1 1  3 2 3 6 . 1 1  2 . 1 . . 1 . . 2 . 2
[17,] 2 1  2 3 2 1 3 1 1 3 5 .  3 1 . . 9 2 1  3 2 1 3 1 4 2 2 2 1 2
[18,] 1 1  2 1 . 1 2 2 2 1 3 .  3 1 . 1 2 4 1  2 1 . . 1 2 . . 1 . 1
[19,] 2 1  2 . . . 1 1 2 3 1 1  1 . 1 1 1 1 5  1 1 . 1 . 1 . 1 1 . 2
[20,] 2 2  2 3 2 2 1 3 3 2 3 1  4 3 3 2 3 2 1 10 2 1 2 1 3 2 . 2 1 2
[21,] 1 1  1 . 1 . . 1 . 2 1 .  1 1 . . 2 1 1  2 4 1 1 1 1 . 1 . 1 .
[22,] 1 .  2 . 1 . . . 1 3 1 1  2 2 1 1 1 . .  1 1 4 2 1 . 1 1 1 . 1
[23,] 2 .  2 3 3 1 1 2 2 3 2 1  1 2 1 . 3 . 1  2 1 2 7 . 2 1 2 2 1 1
[24,] 1 .  1 1 . . 1 2 1 1 2 1  3 . . . 1 1 .  1 1 1 . 4 . 1 1 . . 1
[25,] 4 2  4 2 2 2 2 2 1 2 4 2  3 1 . 1 4 2 1  3 1 . 2 . 9 1 3 2 1 3
[26,] 1 .  1 2 1 1 1 . . 1 2 1  2 . . . 2 . .  2 . 1 1 1 1 3 . 1 1 2
[27,] 2 .  3 . 1 . . 2 1 3 2 .  1 1 1 . 2 . 1  . 1 1 2 1 3 . 6 2 1 1
[28,] 1 .  1 1 3 1 1 . 2 1 3 .  2 1 2 2 2 1 1  2 . 1 2 . 2 1 2 5 1 1
[29,] 1 .  1 1 2 . . 1 . 1 1 .  1 2 . . 1 . .  1 1 . 1 . 1 1 1 1 3 .
[30,] 1 .  3 1 1 2 5 3 1 3 4 1  3 1 1 2 2 1 2  2 . 1 1 1 3 2 1 1 . 9

Matrix^5

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                       
 [1,]  996 324 1256  864 692 487  838 1073 1123  968 1037 391 1411 1040
 [2,]  324  86  394  265 218 159  267  330  326  316  373 136  493  296
 [3,] 1256 394 1496 1167 926 647 1056 1307 1441 1186 1262 494 1777 1312
 [4,]  864 265 1167  630 558 372  709  868  743  918 1055 344 1022  682
 [5,]  692 218  926  558 456 329  684  757  678  835  797 270  870  641
 [6,]  487 159  647  372 329 200  381  441  402  519  641 193  569  363
 [7,]  838 267 1056  709 684 381  666  746  742  861 1098 333 1027  671
 [8,] 1073 330 1307  868 757 441  746  946 1038 1002 1088 453 1247  911
 [9,] 1123 326 1441  743 678 402  742 1038  970 1193 1090 412 1201  970
[10,]  968 316 1186  918 835 519  861 1002 1193  950 1025 404 1493 1108
[11,] 1037 373 1262 1055 797 641 1098 1088 1090 1025 1364 451 1612  975
[12,]  391 136  494  344 270 193  333  453  412  404  451 152  559  388
[13,] 1411 493 1777 1022 870 569 1027 1247 1201 1493 1612 559 1610 1106
[14,] 1040 296 1312  682 641 363  671  911  970 1108  975 388 1106  878
[15,]  680 192  889  456 438 232  451  614  617  793  639 256  728  647
[16,]  645 191  817  447 432 228  441  552  520  780  713 234  688  539
[17,]  956 342 1227  921 749 591 1057 1029 1022  971 1317 422 1522  900
[18,]  652 210  767  530 429 309  504  570  582  614  745 269  851  525
[19,]  487 152  593  447 419 244  406  499  544  478  520 195  740  558
[20,] 1225 361 1569  894 764 518  945 1118 1078 1306 1390 536 1534  999
[21,]  380 130  459  327 274 203  353  370  427  370  411 191  596  368
[22,]  461 162  583  371 338 220  392  463  499  524  470 184  614  480
[23,]  770 246 1055  676 605 401  794  886  857  841  898 318 1088  792
[24,]  433 177  515  358 292 205  322  376  394  401  490 203  541  350
[25,] 1045 357 1307 1046 777 593 1072 1161 1176 1019 1340 429 1619 1015
[26,]  407 150  540  375 309 233  415  437  400  438  588 179  596  356
[27,]  566 221  700  610 464 335  621  643  753  558  607 236  894  682
[28,]  625 213  827  539 437 321  654  664  619  758  761 240  852  624
[29,]  336 110  435  283 222 168  330  357  379  361  370 142  455  314
[30,]  929 315 1135  923 820 486  812  883  940  922 1231 384 1285  849
                                                                          
 [1,] 680 645  956 652 487 1225 380 461  770 433 1045 407 566 625 336  929
 [2,] 192 191  342 210 152  361 130 162  246 177  357 150 221 213 110  315
 [3,] 889 817 1227 767 593 1569 459 583 1055 515 1307 540 700 827 435 1135
 [4,] 456 447  921 530 447  894 327 371  676 358 1046 375 610 539 283  923
 [5,] 438 432  749 429 419  764 274 338  605 292  777 309 464 437 222  820
 [6,] 232 228  591 309 244  518 203 220  401 205  593 233 335 321 168  486
 [7,] 451 441 1057 504 406  945 353 392  794 322 1072 415 621 654 330  812
 [8,] 614 552 1029 570 499 1118 370 463  886 376 1161 437 643 664 357  883
 [9,] 617 520 1022 582 544 1078 427 499  857 394 1176 400 753 619 379  940
[10,] 793 780  971 614 478 1306 370 524  841 401 1019 438 558 758 361  922
[11,] 639 713 1317 745 520 1390 411 470  898 490 1340 588 607 761 370 1231
[12,] 256 234  422 269 195  536 191 184  318 203  429 179 236 240 142  384
[13,] 728 688 1522 851 740 1534 596 614 1088 541 1619 596 894 852 455 1285
[14,] 647 539  900 525 558  999 368 480  792 350 1015 356 682 624 314  849
[15,] 410 339  622 332 339  668 271 371  580 235  653 252 451 391 233  568
[16,] 339 280  739 333 333  652 306 352  600 245  698 276 484 412 236  559
[17,] 622 739 1184 728 519 1241 364 444  791 458 1264 517 598 752 327 1208
[18,] 332 333  728 400 303  713 252 274  503 266  778 299 399 412 217  594
[19,] 339 333  519 303 216  622 219 259  429 210  528 224 297 353 215  435
[20,] 668 652 1241 713 622 1278 462 605  932 543 1331 563 763 733 382 1226
[21,] 271 306  364 252 219  462 134 188  277 174  416 173 202 263 112  402
[22,] 371 352  444 274 259  605 188 246  377 174  473 194 272 324 152  454
[23,] 580 600  791 503 429  932 277 377  644 329  880 347 490 548 262  919
[24,] 235 245  458 266 210  543 174 174  329 160  538 198 239 271 140  391
[25,] 653 698 1264 778 528 1331 416 473  880 538 1248 532 626 736 361 1154
[26,] 252 276  517 299 224  563 173 194  347 198  532 234 255 307 143  520
[27,] 451 484  598 399 297  763 202 272  490 239  626 255 298 413 198  602
[28,] 391 412  752 412 353  733 263 324  548 271  736 307 413 420 220  752
[29,] 233 236  327 217 215  382 112 152  262 140  361 143 198 220  92  392
[30,] 568 559 1208 594 435 1226 402 454  919 391 1154 520 602 752 392  926

Matrix^15

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                      
 [1,] 418109179016 135816352830 526302198801 352517830218 298104869220
 [2,] 135816352830  44118600422 170966561905 114497534385  96826249048
 [3,] 526302198801 170966561905 662473259172 443796203887 375288082254
 [4,] 352517830218 114497534385 443796203887 297014442166 251219059269
 [5,] 298104869220  96826249048 375288082254 251219059269 212470012014
 [6,] 199498169601  64798968959 251152391127 168084573129 142172490656
 [7,] 354982216112 115307269674 446872691430 299153028059 253031699088
 [8,] 412598226770 134010695990 519384797418 347721734063 294104095991
 [9,] 419136940809 136111289187 527654332436 353062262297 298661437842
[10,] 429969647049 139677744551 541204647016 362621049648 306638521919
[11,] 477231665144 155056384756 600730826580 402473047304 340311291377
[12,] 169939583628  55203882712 213918225399 143270365901 121156804386
[13,] 554073940244 179961599684 697520210926 466833497330 394864538153
[14,] 385269430325 125111326355 485011349061 324549815618 274543294461
[15,] 258793285842  84035363167 325794691846 217984205097 184406534192
[16,] 253524015042  82329851738 319168882931 213527664934 180642609967
[17,] 448674348323 145775695165 564796020720 378370666093 319933741248
[18,] 260250585822  84540537803 327610162613 219363502012 185520086449
[19,] 212033813032  68877403015 266891969944 178790405840 151197270686
[20,] 487683818193 158399844198 613940990291 410945875325 347573886141
[21,] 163302740035  53052001506 205559537896 137713254688 116446571923
[22,] 196346491400  63775911289 247160313161 165515529930 139980893358
[23,] 345914280899 112366054473 435449478854 291627330710 246617405867
[24,] 174076415703  56548958253 219127876871 146735961255 124096049887
[25,] 474132063213 154040574578 596827714222 399839170249 338088225012
[26,] 189489638888  61562460778 238538579945 159759548540 135096823645
[27,] 260951499175  84779518982 328460941431 220123185726 186117487763
[28,] 279318766444  90732020455 351629317712 235431939243 199106879155
[29,] 143653975826  46663769185 180838642380 121101640700 102409840112
[30,] 415057237429 134838908100 522464027130 349940777311 295945143234
                                                                      
 [1,] 199498169601 354982216112 412598226770 419136940809 429969647049
 [2,]  64798968959 115307269674 134010695990 136111289187 139677744551
 [3,] 251152391127 446872691430 519384797418 527654332436 541204647016
 [4,] 168084573129 299153028059 347721734063 353062262297 362621049648
 [5,] 142172490656 253031699088 294104095991 298661437842 306638521919
 [6,]  95119243390 169287819722 196764022360 199775670652 205216519018
 [7,] 169287819722 301262263726 350140660481 355548257548 365124282434
 [8,] 196764022360 350140660481 407024465982 413398262466 424354181549
 [9,] 199775670652 355548257548 413398262466 419799857620 431153755272
[10,] 205216519018 365124282434 424354181549 431153755272 442123721522
[11,] 227799462510 405344343944 470953579749 478337071336 490766472105
[12,]  81081007180 144277523419 167687013288 170324680750 174768043070
[13,] 264174420349 470148117312 546510076336 554938197022 569936539159
[14,] 183640293414 326824292076 380011521027 385929746781 396305324661
[15,] 123337424504 219507880765 255247561477 259217547800 266217767783
[16,] 120817775800 215031295716 250008932403 253846828370 260814127929
[17,] 214162430726 381092829662 442775982631 449704007478 461413419181
[18,] 124143021485 220913438191 256745182320 260737220803 267663820872
[19,] 101178206351 180022563150 209235848395 212566395121 218038621848
[20,] 232558392881 413880035380 481082640255 488528603047 501633288990
[21,]  77942644620 138687864407 161168100954 163724670569 167929380618
[22,]  93665875145 166674490502 193742655323 196809122881 201932501385
[23,] 165047896192 293710074318 341350984289 346716461007 355760097489
[24,]  83040992687 147766854503 171735917058 174416383199 179028291549
[25,] 226302161261 402679978770 467901560656 475257714398 487576743519
[26,]  90422301396 160910730678 186969347574 189871899921 194885991998
[27,] 124583228790 221661525642 257582505724 261711964155 268318624413
[28,] 133242194901 237126825323 275586759704 279867372690 287299015084
[29,]  68538625679 121970381961 141756428033 143980374136 147745824324
[30,] 198038651236 352385198327 409499755168 415911285318 426849180441
                                                                      
 [1,] 477231665144 169939583628 554073940244 385269430325 258793285842
 [2,] 155056384756  55203882712 179961599684 125111326355  84035363167
 [3,] 600730826580 213918225399 697520210926 485011349061 325794691846
 [4,] 402473047304 143270365901 466833497330 324549815618 217984205097
 [5,] 340311291377 121156804386 394864538153 274543294461 184406534192
 [6,] 227799462510  81081007180 264174420349 183640293414 123337424504
 [7,] 405344343944 144277523419 470148117312 326824292076 219507880765
 [8,] 470953579749 167687013288 546510076336 380011521027 255247561477
 [9,] 478337071336 170324680750 554938197022 385929746781 259217547800
[10,] 490766472105 174768043070 569936539159 396305324661 266217767783
[11,] 545017459168 193998283035 632547741637 439643941734 295300054015
[12,] 193998283035  69072000124 225182811119 156561440770 105161086036
[13,] 632547741637 225182811119 733730341164 510127792753 342626910149
[14,] 439643941734 156561440770 510127792753 354793182672 238312818565
[15,] 295300054015 105161086036 342626910149 238312818565 160071271910
[16,] 289382463683 103023060931 335601423839 233369738805 156739372726
[17,] 512401708342 182389544114 594684415976 413328514149 277628229035
[18,] 297154896785 105780032312 344766761667 239665788669 160972823218
[19,] 242025148489  86181598431 281002153683 195389902368 131246502402
[20,] 556741204400 198206997063 645913031590 449075949205 301629695419
[21,] 186425522807  66380384249 216455718358 150487381662 101087771664
[22,] 224089477701  79800789772 260154421622 180914627916 121526917819
[23,] 394881061849 140598216741 458375682223 318700807998 214078326501
[24,] 198752934388  70754841532 230618995049 160319684595 107681687192
[25,] 541402532899 192731247320 628421919670 436822258489 293408462292
[26,] 216406723977  77025536235 251091851520 174519035065 117218813777
[27,] 297882179496 106073847296 345972364516 240548776744 161589001232
[28,] 318903768505 113527471879 370040850979 257258648829 172795223493
[29,] 163986699974  58388518510 190349156852 132346322924  88899829340
[30,] 473955000310 168708208993 549956226564 382289234901 256770158931
                                                                      
 [1,] 253524015042 448674348323 260250585822 212033813032 487683818193
 [2,]  82329851738 145775695165  84540537803  68877403015 158399844198
 [3,] 319168882931 564796020720 327610162613 266891969944 613940990291
 [4,] 213527664934 378370666093 219363502012 178790405840 410945875325
 [5,] 180642609967 319933741248 185520086449 151197270686 347573886141
 [6,] 120817775800 214162430726 124143021485 101178206351 232558392881
 [7,] 215031295716 381092829662 220913438191 180022563150 413880035380
 [8,] 250008932403 442775982631 256745182320 209235848395 481082640255
 [9,] 253846828370 449704007478 260737220803 212566395121 488528603047
[10,] 260814127929 461413419181 267663820872 218038621848 501633288990
[11,] 289382463683 512401708342 297154896785 242025148489 556741204400
[12,] 103023060931 182389544114 105780032312  86181598431 198206997063
[13,] 335601423839 594684415976 344766761667 281002153683 645913031590
[14,] 233369738805 413328514149 239665788669 195389902368 449075949205
[15,] 156739372726 277628229035 160972823218 131246502402 301629695419
[16,] 153489972356 272067247877 157702042795 128574808989 295461157738
[17,] 272067247877 481727021592 279372122539 227551356285 523407595558
[18,] 157702042795 279372122539 161982954052 131981602687 303481460672
[19,] 128574808989 227551356285 131981602687 107520862028 247337083452
[20,] 295461157738 523407595558 303481460672 247337083452 568573322242
[21,]  99047224258 175266348977 101668014828  82818429086 190507927679
[22,] 119041234948 210680321341 122197317163  99575857877 228992308060
[23,] 209734029421 371240034702 215319798001 175437511873 403448836844
[24,] 105493510843 186859719022 108348528361  88278598101 203004432731
[25,] 287507318874 509002166499 295204458381 240451257414 553106543329
[26,] 114861109902 203451202705 117971351513  96103321985 221010655228
[27,] 158331991284 280061980749 162478932229 132334193994 304491300537
[28,] 169285405859 299812627899 173852847472 141665616103 325717081852
[29,]  87094974094 154167185885  89417928801  72858819355 167539138144
[30,] 251571427620 445609340630 258367531562 210478849369 484101132512
                                                                      
 [1,] 163302740035 196346491400 345914280899 174076415703 474132063213
 [2,]  53052001506  63775911289 112366054473  56548958253 154040574578
 [3,] 205559537896 247160313161 435449478854 219127876871 596827714222
 [4,] 137713254688 165515529930 291627330710 146735961255 399839170249
 [5,] 116446571923 139980893358 246617405867 124096049887 338088225012
 [6,]  77942644620  93665875145 165047896192  83040992687 226302161261
 [7,] 138687864407 166674490502 293710074318 147766854503 402679978770
 [8,] 161168100954 193742655323 341350984289 171735917058 467901560656
 [9,] 163724670569 196809122881 346716461007 174416383199 475257714398
[10,] 167929380618 201932501385 355760097489 179028291549 487576743519
[11,] 186425522807 224089477701 394881061849 198752934388 541402532899
[12,]  66380384249  79800789772 140598216741  70754841532 192731247320
[13,] 216455718358 260154421622 458375682223 230618995049 628421919670
[14,] 150487381662 180914627916 318700807998 160319684595 436822258489
[15,] 101087771664 121526917819 214078326501 107681687192 293408462292
[16,]  99047224258 119041234948 209734029421 105493510843 287507318874
[17,] 175266348977 210680321341 371240034702 186859719022 509002166499
[18,] 101668014828 122197317163 215319798001 108348528361 295204458381
[19,]  82818429086  99575857877 175437511873  88278598101 240451257414
[20,] 190507927679 228992308060 403448836844 203004432731 553106543329
[21,]  63781194282  76688492166 135109078971  68002247690 185205632091
[22,]  76688492166  92209403388 162441261988  81735731551 222638913194
[23,] 135109078971 162441261988 286185825518 144023022348 392301269324
[24,]  68002247690  81735731551 144023022348  72471529740 197451359394
[25,] 185205632091 222638913194 392301269324 197451359394 537828457348
[26,]  74025876868  88973549265 156782752092  78907609421 214971195906
[27,] 101914771101 122552650481 215916195051 108672377121 295936685833
[28,] 109111573727 131159976232 231089897222 116289345083 316810456511
[29,]  56108556906  67458581629 118844837876  59810365091 162916036489
[30,] 162148369156 194894785144 343443683253 172812481028 470831189621
                                                                      
 [1,] 189489638888 260951499175 279318766444 143653975826 415057237429
 [2,]  61562460778  84779518982  90732020455  46663769185 134838908100
 [3,] 238538579945 328460941431 351629317712 180838642380 522464027130
 [4,] 159759548540 220123185726 235431939243 121101640700 349940777311
 [5,] 135096823645 186117487763 199106879155 102409840112 295945143234
 [6,]  90422301396 124583228790 133242194901  68538625679 198038651236
 [7,] 160910730678 221661525642 237126825323 121970381961 352385198327
 [8,] 186969347574 257582505724 275586759704 141756428033 409499755168
 [9,] 189871899921 261711964155 279867372690 143980374136 415911285318
[10,] 194885991998 268318624413 287299015084 147745824324 426849180441
[11,] 216406723977 297882179496 318903768505 163986699974 473955000310
[12,]  77025536235 106073847296 113527471879  58388518510 168708208993
[13,] 251091851520 345972364516 370040850979 190349156852 549956226564
[14,] 174519035065 240548776744 257258648829 132346322924 382289234901
[15,] 117218813777 161589001232 172795223493  88899829340 256770158931
[16,] 114861109902 158331991284 169285405859  87094974094 251571427620
[17,] 203451202705 280061980749 299812627899 154167185885 445609340630
[18,] 117971351513 162478932229 173852847472  89417928801 258367531562
[19,]  96103321985 132334193994 141665616103  72858819355 210478849369
[20,] 221010655228 304491300537 325717081852 167539138144 484101132512
[21,]  74025876868 101914771101 109111573727  56108556906 162148369156
[22,]  88973549265 122552650481 131159976232  67458581629 194894785144
[23,] 156782752092 215916195051 231089897222 118844837876 343443683253
[24,]  78907609421 108672377121 116289345083  59810365091 172812481028
[25,] 214971195906 295936685833 316810456511 162916036489 470831189621
[26,]  85918001480 118295676113 126605203213  65107494212 188178176425
[27,] 118295676113 162831130124 174380747783  89668078359 259111304851
[28,] 126605203213 174380747783 186584489150  95963340330 277324286514
[29,]  65107494212  89668078359  95963340330  49352229724 142627560213
[30,] 188178176425 259111304851 277324286514 142627560213 412082272270

Matrix^30

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                      
 [1,] 3.590041e+24 1.166153e+24 4.519234e+24 3.026143e+24 2.559265e+24
 [2,] 1.166153e+24 3.788013e+23 1.467982e+24 9.829820e+23 8.313258e+23
 [3,] 4.519234e+24 1.467982e+24 5.688924e+24 3.809385e+24 3.221667e+24
 [4,] 3.026143e+24 9.829820e+23 3.809385e+24 2.550819e+24 2.157274e+24
 [5,] 2.559265e+24 8.313258e+23 3.221667e+24 2.157274e+24 1.824446e+24
 [6,] 1.712554e+24 5.562887e+23 2.155805e+24 1.443558e+24 1.220844e+24
 [7,] 3.047515e+24 9.899241e+23 3.836288e+24 2.568834e+24 2.172510e+24
 [8,] 3.542030e+24 1.150557e+24 4.458796e+24 2.985674e+24 2.525039e+24
 [9,] 3.597441e+24 1.168556e+24 4.528548e+24 3.032381e+24 2.564540e+24
[10,] 3.692290e+24 1.199366e+24 4.647947e+24 3.112331e+24 2.632156e+24
[11,] 4.098446e+24 1.331298e+24 5.159227e+24 3.454692e+24 2.921696e+24
[12,] 1.459149e+24 4.739753e+23 1.836813e+24 1.229957e+24 1.040197e+24
[13,] 4.756240e+24 1.544969e+24 5.987273e+24 4.009165e+24 3.390624e+24
[14,] 3.306790e+24 1.074144e+24 4.162670e+24 2.787384e+24 2.357342e+24
[15,] 2.221126e+24 7.214883e+23 2.796009e+24 1.872248e+24 1.583394e+24
[16,] 2.175895e+24 7.067959e+23 2.739071e+24 1.834122e+24 1.551150e+24
[17,] 3.853171e+24 1.251625e+24 4.850468e+24 3.247943e+24 2.746845e+24
[18,] 2.234424e+24 7.258079e+23 2.812749e+24 1.883457e+24 1.592874e+24
[19,] 1.820662e+24 5.914056e+23 2.291895e+24 1.534686e+24 1.297912e+24
[20,] 4.186592e+24 1.359930e+24 5.270186e+24 3.528993e+24 2.984533e+24
[21,] 1.402351e+24 4.555255e+23 1.765314e+24 1.182080e+24 9.997064e+23
[22,] 1.685783e+24 5.475926e+23 2.122105e+24 1.420992e+24 1.201759e+24
[23,] 2.970192e+24 9.648071e+23 3.738952e+24 2.503656e+24 2.117387e+24
[24,] 1.494580e+24 4.854844e+23 1.881415e+24 1.259823e+24 1.065455e+24
[25,] 4.071671e+24 1.322601e+24 5.125522e+24 3.432123e+24 2.902609e+24
[26,] 1.627154e+24 5.285483e+23 2.048302e+24 1.371573e+24 1.159964e+24
[27,] 2.241128e+24 7.279854e+23 2.821188e+24 1.889108e+24 1.597653e+24
[28,] 2.398194e+24 7.790051e+23 3.018906e+24 2.021503e+24 1.709622e+24
[29,] 1.233453e+24 4.006626e+23 1.552702e+24 1.039712e+24 8.793031e+23
[30,] 3.563930e+24 1.157671e+24 4.486364e+24 3.004134e+24 2.540651e+24
                                                                      
 [1,] 1.712554e+24 3.047515e+24 3.542030e+24 3.597441e+24 3.692290e+24
 [2,] 5.562887e+23 9.899241e+23 1.150557e+24 1.168556e+24 1.199366e+24
 [3,] 2.155805e+24 3.836288e+24 4.458796e+24 4.528548e+24 4.647947e+24
 [4,] 1.443558e+24 2.568834e+24 2.985674e+24 3.032381e+24 3.112331e+24
 [5,] 1.220844e+24 2.172510e+24 2.525039e+24 2.564540e+24 2.632156e+24
 [6,] 8.169379e+23 1.453753e+24 1.689651e+24 1.716084e+24 1.761329e+24
 [7,] 1.453753e+24 2.586976e+24 3.006760e+24 3.053797e+24 3.134312e+24
 [8,] 1.689651e+24 3.006760e+24 3.494661e+24 3.549331e+24 3.642911e+24
 [9,] 1.716084e+24 3.053797e+24 3.549331e+24 3.604856e+24 3.699900e+24
[10,] 1.761329e+24 3.134312e+24 3.642911e+24 3.699900e+24 3.797450e+24
[11,] 1.955078e+24 3.479091e+24 4.043637e+24 4.106894e+24 4.215175e+24
[12,] 6.960564e+23 1.238643e+24 1.439635e+24 1.462157e+24 1.500707e+24
[13,] 2.268865e+24 4.037479e+24 4.692633e+24 4.766044e+24 4.891702e+24
[14,] 1.577435e+24 2.807069e+24 3.262568e+24 3.313607e+24 3.400971e+24
[15,] 1.059542e+24 1.885471e+24 2.191423e+24 2.225705e+24 2.284386e+24
[16,] 1.037965e+24 1.847075e+24 2.146796e+24 2.180380e+24 2.237867e+24
[17,] 1.838074e+24 3.270881e+24 3.801641e+24 3.861113e+24 3.962914e+24
[18,] 1.065885e+24 1.896759e+24 2.204543e+24 2.239030e+24 2.298063e+24
[19,] 8.685087e+23 1.545524e+24 1.796314e+24 1.824415e+24 1.872517e+24
[20,] 1.997126e+24 3.553915e+24 4.130603e+24 4.195221e+24 4.305830e+24
[21,] 6.689619e+23 1.190428e+24 1.383597e+24 1.405241e+24 1.442291e+24
[22,] 8.041672e+23 1.431028e+24 1.663238e+24 1.689257e+24 1.733796e+24
[23,] 1.416868e+24 2.521337e+24 2.930470e+24 2.976314e+24 3.054786e+24
[24,] 7.129582e+23 1.268720e+24 1.474593e+24 1.497661e+24 1.537148e+24
[25,] 1.942305e+24 3.456361e+24 4.017219e+24 4.080064e+24 4.187637e+24
[26,] 7.761997e+23 1.381259e+24 1.605394e+24 1.630508e+24 1.673497e+24
[27,] 1.069083e+24 1.902449e+24 2.211156e+24 2.245747e+24 2.304958e+24
[28,] 1.144008e+24 2.035780e+24 2.366122e+24 2.403137e+24 2.466497e+24
[29,] 5.883931e+23 1.047054e+24 1.216958e+24 1.235996e+24 1.268584e+24
[30,] 1.700098e+24 3.025350e+24 3.516268e+24 3.571276e+24 3.665435e+24
                                                                      
 [1,] 4.098446e+24 1.459149e+24 4.756240e+24 3.306790e+24 2.221126e+24
 [2,] 1.331298e+24 4.739753e+23 1.544969e+24 1.074144e+24 7.214883e+23
 [3,] 5.159227e+24 1.836813e+24 5.987273e+24 4.162670e+24 2.796009e+24
 [4,] 3.454692e+24 1.229957e+24 4.009165e+24 2.787384e+24 1.872248e+24
 [5,] 2.921696e+24 1.040197e+24 3.390624e+24 2.357342e+24 1.583394e+24
 [6,] 1.955078e+24 6.960564e+23 2.268865e+24 1.577435e+24 1.059542e+24
 [7,] 3.479091e+24 1.238643e+24 4.037479e+24 2.807069e+24 1.885471e+24
 [8,] 4.043637e+24 1.439635e+24 4.692633e+24 3.262568e+24 2.191423e+24
 [9,] 4.106894e+24 1.462157e+24 4.766044e+24 3.313607e+24 2.225705e+24
[10,] 4.215175e+24 1.500707e+24 4.891702e+24 3.400971e+24 2.284386e+24
[11,] 4.678850e+24 1.665787e+24 5.429797e+24 3.775083e+24 2.535672e+24
[12,] 1.665787e+24 5.930618e+23 1.933143e+24 1.344024e+24 9.027625e+23
[13,] 5.429797e+24 1.933143e+24 6.301270e+24 4.380977e+24 2.942643e+24
[14,] 3.775083e+24 1.344024e+24 4.380977e+24 3.045888e+24 2.045882e+24
[15,] 2.535672e+24 9.027625e+23 2.942643e+24 2.045882e+24 1.374191e+24
[16,] 2.484036e+24 8.843786e+23 2.882719e+24 2.004219e+24 1.346207e+24
[17,] 4.398840e+24 1.566097e+24 5.104846e+24 3.549160e+24 2.383923e+24
[18,] 2.550853e+24 9.081674e+23 2.960261e+24 2.058131e+24 1.382418e+24
[19,] 2.078496e+24 7.399965e+23 2.412091e+24 1.677014e+24 1.126427e+24
[20,] 4.779478e+24 1.701613e+24 5.546576e+24 3.856274e+24 2.590207e+24
[21,] 1.600945e+24 5.699764e+23 1.857894e+24 1.291707e+24 8.676219e+23
[22,] 1.924516e+24 6.851755e+23 2.233397e+24 1.552776e+24 1.042979e+24
[23,] 3.390817e+24 1.207215e+24 3.935037e+24 2.735846e+24 1.837631e+24
[24,] 1.706236e+24 6.074626e+23 1.980084e+24 1.376660e+24 9.246836e+23
[25,] 4.648283e+24 1.654905e+24 5.394324e+24 3.750420e+24 2.519107e+24
[26,] 1.857584e+24 6.613463e+23 2.155723e+24 1.498773e+24 1.006706e+24
[27,] 2.558506e+24 9.108920e+23 2.969142e+24 2.064305e+24 1.386566e+24
[28,] 2.737815e+24 9.747305e+23 3.177230e+24 2.208979e+24 1.483741e+24
[29,] 1.408130e+24 5.013292e+23 1.634132e+24 1.136135e+24 7.631267e+23
[30,] 4.068638e+24 1.448536e+24 4.721647e+24 3.282740e+24 2.204972e+24
                                                                      
 [1,] 2.175895e+24 3.853171e+24 2.234424e+24 1.820662e+24 4.186592e+24
 [2,] 7.067959e+23 1.251625e+24 7.258079e+23 5.914056e+23 1.359930e+24
 [3,] 2.739071e+24 4.850468e+24 2.812749e+24 2.291895e+24 5.270186e+24
 [4,] 1.834122e+24 3.247943e+24 1.883457e+24 1.534686e+24 3.528993e+24
 [5,] 1.551150e+24 2.746845e+24 1.592874e+24 1.297912e+24 2.984533e+24
 [6,] 1.037965e+24 1.838074e+24 1.065885e+24 8.685087e+23 1.997126e+24
 [7,] 1.847075e+24 3.270881e+24 1.896759e+24 1.545524e+24 3.553915e+24
 [8,] 2.146796e+24 3.801641e+24 2.204543e+24 1.796314e+24 4.130603e+24
 [9,] 2.180380e+24 3.861113e+24 2.239030e+24 1.824415e+24 4.195221e+24
[10,] 2.237867e+24 3.962914e+24 2.298063e+24 1.872517e+24 4.305830e+24
[11,] 2.484036e+24 4.398840e+24 2.550853e+24 2.078496e+24 4.779478e+24
[12,] 8.843786e+23 1.566097e+24 9.081674e+23 7.399965e+23 1.701613e+24
[13,] 2.882719e+24 5.104846e+24 2.960261e+24 2.412091e+24 5.546576e+24
[14,] 2.004219e+24 3.549160e+24 2.058131e+24 1.677014e+24 3.856274e+24
[15,] 1.346207e+24 2.383923e+24 1.382418e+24 1.126427e+24 2.590207e+24
[16,] 1.318793e+24 2.335376e+24 1.354267e+24 1.103489e+24 2.537460e+24
[17,] 2.335376e+24 4.135587e+24 2.398195e+24 1.954107e+24 4.493446e+24
[18,] 1.354267e+24 2.398195e+24 1.390695e+24 1.133171e+24 2.605715e+24
[19,] 1.103489e+24 1.954107e+24 1.133171e+24 9.233352e+23 2.123198e+24
[20,] 2.537460e+24 4.493446e+24 2.605715e+24 2.123198e+24 4.882271e+24
[21,] 8.499535e+23 1.505135e+24 8.728163e+23 7.111916e+23 1.635377e+24
[22,] 1.021739e+24 1.809341e+24 1.049223e+24 8.549320e+23 1.965906e+24
[23,] 1.800209e+24 3.187890e+24 1.848633e+24 1.506310e+24 3.463743e+24
[24,] 9.058533e+23 1.604125e+24 9.302197e+23 7.579652e+23 1.742932e+24
[25,] 2.467807e+24 4.370102e+24 2.534189e+24 2.064917e+24 4.748254e+24
[26,] 9.862051e+23 1.746415e+24 1.012733e+24 8.251989e+23 1.897535e+24
[27,] 1.358330e+24 2.405390e+24 1.394867e+24 1.136571e+24 2.613532e+24
[28,] 1.453526e+24 2.573968e+24 1.492624e+24 1.216226e+24 2.796698e+24
[29,] 7.475863e+23 1.323859e+24 7.676955e+23 6.255366e+23 1.438414e+24
[30,] 2.160070e+24 3.825146e+24 2.218173e+24 1.807420e+24 4.156142e+24
                                                                      
 [1,] 1.402351e+24 1.685783e+24 2.970192e+24 1.494580e+24 4.071671e+24
 [2,] 4.555255e+23 5.475926e+23 9.648071e+23 4.854844e+23 1.322601e+24
 [3,] 1.765314e+24 2.122105e+24 3.738952e+24 1.881415e+24 5.125522e+24
 [4,] 1.182080e+24 1.420992e+24 2.503656e+24 1.259823e+24 3.432123e+24
 [5,] 9.997064e+23 1.201759e+24 2.117387e+24 1.065455e+24 2.902609e+24
 [6,] 6.689619e+23 8.041672e+23 1.416868e+24 7.129582e+23 1.942305e+24
 [7,] 1.190428e+24 1.431028e+24 2.521337e+24 1.268720e+24 3.456361e+24
 [8,] 1.383597e+24 1.663238e+24 2.930470e+24 1.474593e+24 4.017219e+24
 [9,] 1.405241e+24 1.689257e+24 2.976314e+24 1.497661e+24 4.080064e+24
[10,] 1.442291e+24 1.733796e+24 3.054786e+24 1.537148e+24 4.187637e+24
[11,] 1.600945e+24 1.924516e+24 3.390817e+24 1.706236e+24 4.648283e+24
[12,] 5.699764e+23 6.851755e+23 1.207215e+24 6.074626e+23 1.654905e+24
[13,] 1.857894e+24 2.233397e+24 3.935037e+24 1.980084e+24 5.394324e+24
[14,] 1.291707e+24 1.552776e+24 2.735846e+24 1.376660e+24 3.750420e+24
[15,] 8.676219e+23 1.042979e+24 1.837631e+24 9.246836e+23 2.519107e+24
[16,] 8.499535e+23 1.021739e+24 1.800209e+24 9.058533e+23 2.467807e+24
[17,] 1.505135e+24 1.809341e+24 3.187890e+24 1.604125e+24 4.370102e+24
[18,] 8.728163e+23 1.049223e+24 1.848633e+24 9.302197e+23 2.534189e+24
[19,] 7.111916e+23 8.549320e+23 1.506310e+24 7.579652e+23 2.064917e+24
[20,] 1.635377e+24 1.965906e+24 3.463743e+24 1.742932e+24 4.748254e+24
[21,] 5.477898e+23 6.585046e+23 1.160224e+24 5.838167e+23 1.590486e+24
[22,] 6.585046e+23 7.915962e+23 1.394719e+24 7.018130e+23 1.911943e+24
[23,] 1.160224e+24 1.394719e+24 2.457364e+24 1.236529e+24 3.368665e+24
[24,] 5.838167e+23 7.018130e+23 1.236529e+24 6.222131e+23 1.695089e+24
[25,] 1.590486e+24 1.911943e+24 3.368665e+24 1.695089e+24 4.617916e+24
[26,] 6.356029e+23 7.640659e+23 1.346213e+24 6.774052e+23 1.845449e+24
[27,] 8.754350e+23 1.052371e+24 1.854179e+24 9.330104e+23 2.541792e+24
[28,] 9.367884e+23 1.126125e+24 1.984126e+24 9.983991e+23 2.719929e+24
[29,] 4.818147e+23 5.791952e+23 1.020488e+24 5.135026e+23 1.398930e+24
[30,] 1.392151e+24 1.673522e+24 2.948589e+24 1.483710e+24 4.042057e+24
                                                                      
 [1,] 1.627154e+24 2.241128e+24 2.398194e+24 1.233453e+24 3.563930e+24
 [2,] 5.285483e+23 7.279854e+23 7.790051e+23 4.006626e+23 1.157671e+24
 [3,] 2.048302e+24 2.821188e+24 3.018906e+24 1.552702e+24 4.486364e+24
 [4,] 1.371573e+24 1.889108e+24 2.021503e+24 1.039712e+24 3.004134e+24
 [5,] 1.159964e+24 1.597653e+24 1.709622e+24 8.793031e+23 2.540651e+24
 [6,] 7.761997e+23 1.069083e+24 1.144008e+24 5.883931e+23 1.700098e+24
 [7,] 1.381259e+24 1.902449e+24 2.035780e+24 1.047054e+24 3.025350e+24
 [8,] 1.605394e+24 2.211156e+24 2.366122e+24 1.216958e+24 3.516268e+24
 [9,] 1.630508e+24 2.245747e+24 2.403137e+24 1.235996e+24 3.571276e+24
[10,] 1.673497e+24 2.304958e+24 2.466497e+24 1.268584e+24 3.665435e+24
[11,] 1.857584e+24 2.558506e+24 2.737815e+24 1.408130e+24 4.068638e+24
[12,] 6.613463e+23 9.108920e+23 9.747305e+23 5.013292e+23 1.448536e+24
[13,] 2.155723e+24 2.969142e+24 3.177230e+24 1.634132e+24 4.721647e+24
[14,] 1.498773e+24 2.064305e+24 2.208979e+24 1.136135e+24 3.282740e+24
[15,] 1.006706e+24 1.386566e+24 1.483741e+24 7.631267e+23 2.204972e+24
[16,] 9.862051e+23 1.358330e+24 1.453526e+24 7.475863e+23 2.160070e+24
[17,] 1.746415e+24 2.405390e+24 2.573968e+24 1.323859e+24 3.825146e+24
[18,] 1.012733e+24 1.394867e+24 1.492624e+24 7.676955e+23 2.218173e+24
[19,] 8.251989e+23 1.136571e+24 1.216226e+24 6.255366e+23 1.807420e+24
[20,] 1.897535e+24 2.613532e+24 2.796698e+24 1.438414e+24 4.156142e+24
[21,] 6.356029e+23 8.754350e+23 9.367884e+23 4.818147e+23 1.392151e+24
[22,] 7.640659e+23 1.052371e+24 1.126125e+24 5.791952e+23 1.673522e+24
[23,] 1.346213e+24 1.854179e+24 1.984126e+24 1.020488e+24 2.948589e+24
[24,] 6.774052e+23 9.330104e+23 9.983991e+23 5.135026e+23 1.483710e+24
[25,] 1.845449e+24 2.541792e+24 2.719929e+24 1.398930e+24 4.042057e+24
[26,] 7.374930e+23 1.015771e+24 1.086960e+24 5.590518e+23 1.615319e+24
[27,] 1.015771e+24 1.399052e+24 1.497102e+24 7.699987e+23 2.224828e+24
[28,] 1.086960e+24 1.497102e+24 1.602025e+24 8.239629e+23 2.380751e+24
[29,] 5.590518e+23 7.699987e+23 8.239629e+23 4.237855e+23 1.224482e+24
[30,] 1.615319e+24 2.224828e+24 2.380751e+24 1.224482e+24 3.538009e+24

E) Radius, Diameter and Girth

Eccentricity

 [1] 3 3 2 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Radius

[1] 2

Diameter

[1] 3

Girth

$girth
[1] 3

$circle
+ 3/30 vertices, from 1769def:
[1] 3 1 8

F) Density

Density

[1] 0.2206897

G) Induced Graph

H)degree, pathesLength, edge avarage

degree’s average

[1] 6.4

avarage of pathes length

[1] 1.951724

edge’s avarage

[1] 3.2

I)clustering coefficient

local clustering coefficient

 [1] 0.42857143 0.00000000 0.26666667 0.26666667 0.20000000 0.33333333
 [7] 0.23809524 0.28571429 0.28571429 0.19444444 0.36111111 0.16666667
[13] 0.21818182 0.28571429 0.40000000 0.06666667 0.30555556 0.66666667
[19] 0.10000000 0.22222222 0.16666667 0.50000000 0.23809524 0.16666667
[25] 0.27777778 1.00000000 0.06666667 0.30000000 0.00000000 0.19444444

local Clustering Coefficient Avarage

[1] 0.2734103

global clustering coefficient

[1] 0.2582781

A)erdosRenyi Graph With Direction

B)Transposed

C)Subdivision Graph

---

+ 226/226 edges from 17ee3db:
  [1]  3->31 31-> 1  9->32 32-> 1 19->33 33-> 1 26->34 34-> 1  2->35 35->30
 [11] 16->36 36-> 2 30->37 37-> 2  1->38 38-> 3 15->39 39-> 3 20->40 40-> 3
 [21] 27->41 41-> 3 29->42 42-> 3  5->43 43-> 4 22->44 44-> 4 10->45 45-> 5
 [31] 14->46 46-> 5 19->47 47-> 5 22->48 48-> 5 23->49 49-> 5 27->50 50-> 5
 [41]  5->51 51-> 6 10->52 52-> 6 16->53 53-> 6 23->54 54-> 6 25->55 55-> 6
 [51] 29->56 56-> 6 21->57 57-> 7 25->58 58-> 7  7->59 59-> 8 10->60 60-> 8
 [61] 27->61 61-> 8  9->62 62->30 26->63 63-> 9  6->64 64->10 10->65 65->30
 [71] 14->66 66->10 16->67 67->10 20->68 68->10 11->69 69->30 19->70 70->11
 [81] 25->71 71->11 26->72 72->11 27->73 73->11 30->74 74->11  4->75 75->12
 [91] 11->76 76->12 18->77 77->12 21->78 78->12 22->79 79->12 23->80 80->12
+ ... omitted several edges

D)Hamiltonian Cycle

 [1]  1  3 15  2 30  9 26 11 19  5  4 22 12 18 14 10 20 16  6 29  7 23 25
[24] 27 21 24  8 17 28 13

E)Adjecency Matrix

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                 
 [1,] . . 1 . . . . . . . . . 1 . . . . 1 . . . . . . . . 1 . . .
 [2,] . . . . . . . . . . . . 1 . 1 . . . . . . . . . . 1 . 1 . 1
 [3,] 1 . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . .
 [4,] . . . . . . . . . . . 1 . . . . . . . . 1 . . . . . . . . .
 [5,] . . . 1 . 1 . . . . . . . . . . . . . . . . . . . 1 . 1 . .
 [6,] . . . . . . . . . 1 . . 1 . . . . . 1 . . . . . . . . . . .
 [7,] . . . . . . . 1 . . . . . . . . . . . . 1 1 1 . . . . . 1 .
 [8,] . . . . . . . . . . . . . 1 . . 1 . . . . . . 1 . . . . . .
 [9,] 1 . . . . . . . . . . . . . . . 1 . . . 1 . . . . . . . . 1
[10,] . . . . 1 1 . 1 . . . . 1 . . 1 . . . . . . . . . . . . . 1
[11,] . . . . . . . . . . . 1 . . . . . . 1 . . . . . . . . . . 1
[12,] . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . .
[13,] . . . . . . . . . . . . . 1 . . 1 . . . . . . . . . . 1 . .
[14,] . . . . 1 . . . . 1 . . . . . . . . . . . 1 . 1 . . . 1 . .
[15,] . . 1 . . . . . . . . . . . . . . . . . . . . . . 1 . . . 1
[16,] . 1 . . . 1 . . . 1 . . . . . . . 1 . . . . 1 . . . . . . .
[17,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[18,] . . . . . . . . . . . 1 . 1 . . . . . 1 . . . . . . 1 . . .
[19,] 1 . . . 1 . . . . . 1 . 1 . . . . . . . . . . . . . . . . .
[20,] . . 1 . . . . . . 1 . . . . . 1 . . . . . . . . . . . . . .
[21,] . . . . . . 1 . . . . 1 . . . . . . . . . . . . . 1 1 . 1 .
[22,] . . . 1 1 . . . . . . 1 . . . . . . . 1 . . . . . . . . . .
[23,] . . . . 1 1 . . . . . 1 . . . . . . 1 . . . . . 1 . . . . .
[24,] . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . .
[25,] . . . . . 1 1 . . . 1 . . 1 . . . . . . . . 1 . . . . . . .
[26,] 1 . . . . . . . 1 . 1 . . . . . . . . . . . . 1 . . . . . .
[27,] . . 1 . 1 . . 1 . . 1 . . . . . . 1 . . . . . . 1 1 . . . .
[28,] . . . . . . . . . . . . . . . 1 1 . 1 . . . . . . . . . . .
[29,] . . 1 . . 1 . . . . . . . . . . . . . . . . . . . . . . . .
[30,] . 1 . . . . . . . . 1 1 . . . 1 1 . . 1 . . . . . . 1 . 1 .

F)Radius, Diameter and Girth

Eccentricity

 [1] 3 3 3 3 2 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2 2 3 3 3

Radius

[1] 2

Diameter

[1] 6

Girth

$girth
[1] 3

$circle
+ 3/30 vertices, from 17be05e:
[1]  3  1 26

G)Induced Graph

H)degree, pathesLength, edge avarage

degree’s average

[1] 3.766667

avarage of pathes length

[1] 3.496552

edge’s avarage

[1] 3.766667

I)clustering coefficient

local clustering coefficient

 [1] 0.2142857 0.2380952 0.1904762 0.5000000 0.2222222 0.2500000 0.0952381
 [8] 0.1333333 0.3000000 0.2000000 0.1428571 0.1071429 0.2857143 0.1944444
[15] 0.5000000 0.2222222 0.2000000 0.0952381 0.2500000 0.2666667 0.1388889
[22] 0.2000000 0.1666667 0.3333333 0.1428571 0.2444444 0.1636364 0.3333333
[29] 0.1000000 0.1025641

local Clustering Coefficient Avarage

[1] 0.2734103

global clustering coefficient

[1] 0.2385321

A)erdosRenyi Graph With Direction and wieght

      [,1] [,2] [,3]
 [1,]    8    1   16
 [2,]   11    1   21
 [3,]   21    1   74
 [4,]    3    2   81
 [5,]   10    2   41
 [6,]   14    2   97
 [7,]   22    2   39
 [8,]    2    3   12
 [9,]    9    3   14
[10,]   19    3   76
[11,]   26    3   88
[12,]   13    4    9
[13,]   18    4   72
[14,]   20    4   65
[15,]   26    4   43
[16,]   11    5   75
[17,]    1    6   83
[18,]   12    7   50
[19,]   16    7   76
[20,]   21    7    6
[21,]    5    8   76
[22,]    6    8   82
[23,]   12    8   28
[24,]   13    8   27
[25,]   14    8   44
[26,]   30    8   66
[27,]   20    9   96
[28,]    6   10   72
[29,]   13   10    6
[30,]    8   11   55
[31,]   22   11   42
[32,]    9   12   58
[33,]   20   12   26
[34,]   10   13   51
[35,]   13   30   41
[36,]   27   13   11
[37,]   12   14   64
[38,]   15   14   12
[39,]   23   14   55
[40,]   25   14   45
[41,]    8   15    5
[42,]   25   15   40
[43,]   18   16   70
[44,]   23   16   64
[45,]   25   16   64
[46,]   27   16   11
[47,]   10   17   12
[48,]   14   17   37
[49,]    1   18   42
[50,]    4   18   62
[51,]    6   18   60
[52,]   10   18   27
[53,]    7   19   40
[54,]    8   19   51
[55,]   12   19   58
[56,]   15   19   40
[57,]   24   19   30
[58,]   26   19   98
[59,]   26   20   66
[60,]    7   21   38
[61,]   19   22   86
[62,]   30   23   88
[63,]    5   24   71
[64,]    1   25   66
[65,]   16   25   89
[66,]   28   25   58
[67,]   17   26   93
[68,]   18   26   51
[69,]   27   26   50
[70,]    5   27   95
[71,]   19   27   69
[72,]   17   28    1
[73,]   19   28   35
[74,]   20   28   46
[75,]    2   29   63
[76,]   10   29   53
[77,]   19   29   84
[78,]   24   29   72

B)subGraph

      [,1] [,2] [,3]
 [1,]    8    1   16
 [2,]   11    1   21
 [3,]    2    3   12
 [4,]    9    3   14
 [5,]   13    4    9
 [6,]   21    7    6
 [7,]   12    8   28
 [8,]   13    8   27
 [9,]   13   10    6
[10,]   20   12   26
[11,]   27   13   11
[12,]   15   14   12
[13,]    8   15    5
[14,]   27   16   11
[15,]   10   17   12
[16,]   10   18   27
[17,]   17   28    1

C)MST

      [,1] [,2] [,3]
 [1,]    8    1   16
 [2,]   11    1   21
 [3,]   10    2   41
 [4,]   22    2   39
 [5,]    2    3   12
 [6,]    9    3   14
 [7,]   13    4    9
 [8,]   26    4   43
 [9,]   21    7    6
[10,]   12    8   28
[11,]   13    8   27
[12,]   13   10    6
[13,]   20   12   26
[14,]   13   30   41
[15,]   27   13   11
[16,]   15   14   12
[17,]   23   14   55
[18,]    8   15    5
[19,]   25   15   40
[20,]   27   16   11
[21,]   10   17   12
[22,]    6   18   60
[23,]   10   18   27
[24,]    7   19   40
[25,]   24   19   30
[26,]    5   24   71
[27,]   17   28    1
[28,]   19   28   35
[29,]   10   29   53

D) Radius, Diameter, Girth

Eccentricity

 [1] 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 4 3 4 4 3 3 3 3 3 3

Radius

[1] 3

Diameter

[1] 434

Girth

$girth
[1] 3

$circle
+ 3/30 vertices, from 181a95c:
[1] 6 1 8

E)degree, pathesLength, edge avarage

degree’s average

[1] 136

avarage of pathes length

[1] 5.726437

edge’s avarage

[1] 2.6

F)clustering coefficient

local clustering coefficient

 [1] 0.20000000 0.06666667 0.10000000 0.20000000 0.16666667 0.50000000
 [7] 0.10000000 0.17777778 0.33333333 0.09523810 0.33333333 0.26666667
[13] 0.06666667 0.14285714 0.50000000 0.00000000 0.00000000 0.14285714
[19] 0.10909091 0.20000000 0.00000000 0.00000000 0.00000000 0.33333333
[25] 0.06666667 0.19047619 0.10000000 0.00000000 0.33333333 0.33333333

local Clustering Coefficient Avarage

[1] 0.1840067

global clustering coefficient

[1] 0.1686391

A) Multi Graph

B)degree, pathesLength, edge avarage

degree’s average

[1] 3.733333

avarage of pathes length

[1] 1.628571

edge’s avarage

[1] 1.866667

C)clustering coefficient

local clustering coefficient

 [1] 0.05747126 0.18382353 0.50000000 0.50000000 0.50000000 0.50000000
 [7] 0.50000000 0.50000000 0.50000000 0.50000000 0.50000000 0.50000000
[13] 0.50000000 0.50000000 0.18382353

local Clustering Coefficient Avarage

[1] 0.8549451

global clustering coefficient

[1] 0.3592233

A.1) Watts Strogatz Graph With 30 Node

A.2)degree, pathesLength, edge avarage

degree’s average

[1] 8

avarage of pathes length

[1] 1.806897

edge’s avarage

[1] 4

A.3)clustering coefficient

local clustering coefficient

 [1] 0.3333333 0.2500000 0.2380952 0.0000000 0.2000000 0.3333333 0.1904762
 [8] 0.3571429 0.3928571 0.2500000 0.2948718 0.2857143 0.2222222 0.0000000
[15] 0.3333333 0.2500000 0.3000000 0.0000000 0.3000000 0.2575758 0.2444444
[22] 0.2545455 0.3555556 0.2000000 0.1777778 0.1785714 0.3555556 0.3111111
[29] 0.2857143 0.2380952

local Clustering Coefficient Avarage

[1] 0.2463442

global clustering coefficient

[1] 0.2700965

B.1) Watts Strogatz Graph With 1000 Node

B.2)degree, pathesLength, edge avarage

degree’s average

[1] 8

avarage of pathes length

[1] 3.550472

edge’s avarage

[1] 4

B.3)clustering coefficient

local Clustering Coefficient Avarage

[1] 0.007218818

global clustering coefficient

[1] 0.007229368

C.1) Watts Strogatz Graph With 10000 Nodes (Zoomed)

C.2) Watts Strogatz Graph With 10000 Nodes

C.3)degree, pathesLength, edge avarage

degree’s average

[1] 8

avarage of pathes length

[1] 12.66071

edge’s avarage

[1] 4

C.3)clustering coefficient

local Clustering Coefficient Avarage

[1] 0.0007714842

global clustering coefficient

[1] 0.0007612329

A.1) Snobbish Complex Network With 60 Node

A.2)degree avarage, Histogram

degree’s average

[1] 14.9

Histogram

B.1)blue subgraph

blueGraph

B.2)blue subgraph degree

degree’s average

[1] 1497.4

Histogram

C.1) Snobbish Complex Network With 600 Node

C.2)degree average, Histogram

degree’s average

[1] 156.21

Histogram

A.1)Barabasi Albert Graph